C₂×C₂₉×#410 #16816596

order	3712
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₉ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

direct product

C₂×C₂₉×#410

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂²⋊C₄
commutator	C₂²	C₂³×C₄×C₂₉
Frattini, cosocle	C₂³	C₂⁴×C₂₉
socle	C₂²×C₂₉	C₂×C₂²⋊C₄
prime radical	C₂²×#41×C₂₉	C₂
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₂³×C₄×C₂₉ ◁ G

788 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 928

A minimal faithful permutation representation — 4 generators on 47 points:

(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47);(3,4)(5,11,13,8)(6,9)(7,10)(12,17,18,15)(14,16);(3,5)(4,8)(6,12)(7,13)(9,15)(10,11)(14,18)(16,17);(3,6,7,14)(4,9,10,16)(5,12,13,18)(8,15,11,17)

Conjugacy classes & character table

1276 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#10742, C₂₉×#10743, C₂₉×#10748, …
maximal normal subgroup of	C₂₉×#10742, C₂₉×#10743, C₂₉×#10748, …
maximal quotient of	C₂×C₂₉×#1458, C₂×C₂₉×#1460, C₂×C₂₉×#1461, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1614);

C2×C29×#410 #16816596